Chris, would a laser operating in IR frequencies not be able to deliver a pulse or continuous beam strong enough to overload the camera in the seeker head of the missile, much in the same way that a flashbang works on people? I know people and cameras are different, but if you point a camera at a target with sufficient ambient light, the image is washed out, I would think that this would work similarly on an IR camera.
As for the melting thing; so long as the lens could withstand the heat of the laser, a directed beam with minimal diffusion could well be powerful enough to either overload the sensor, or outright melt some of its more delicate parts, either should be enough to disable the missile. I, however, have no idea how powerful a laser you would need for this, and weather or not satisfactory materials exist or could be produced in a timely fashion.
The other problem is the power source. The 747 modified to carry the military experimental anti-missile laser system needs the majority of its cargo hold to be filled with large, specialized, liquid chemical tanks for the electrochemical reaction of the magnitude needed.